What are volcanoes made of? How do they grow?

An intrusion is magma that moves up into a volcano without erupting. Like a balloon, this causes the volcano grows on the inside.

An extrusion is an eruption of material that causes the volcano to grow on the outside.

Volcanoes are constructed this way mainly of two materials: lava and ash. Both of these volcanic products come in many different variations and different volcanoes have different proportions of them. For example, shield volcanoes (such as those in Hawai'i and the Galapagos) are probably >95% lava and only ~5% ash (in the form of cinder). Furthermore, the basaltic lava that makes up shield volcanoes is very fluid and cannot be piled up into steep mounds. This is why shield volcanoes have very gradual slopes.

Another kind of volcano is called either a stratovolcano or composite-volcano. Mt. St. Helens, Pinatubo, and Fuji are all stratovolcanoes. Stratovolcanoes have a higher proportion of ash, and perhaps are up to 50/50 lava and ash. Ash is loose and can be piled up to slopes up to 30 degrees. Additionally, these stratovolcanoes erupt much more viscous lava than basalt, and this highly viscous lava doesn't flow very well (the Mt. St. Helens lava dome is an example of this lava). Because of the combination of viscous lava and ash, stratovolcanoes are much steeper than shield volcanoes.